ABSTRACT
Mathematicians and philosophers of mathematics have long claimed exclusive jurisdiction over inquiries into the nature of mathematical knowledge. Their inquiries have been based on the following sorts of assumptions: that Platonic and Pythagorean conceptions of mathematics are valid, intelligible, and useful; that mathematical statements transcend the flux of history; that mathematics is a creation of pure thought; and that the secret of mathematical power lies in the formal relations among symbols. The language used to talk about the nature of mathematical knowledge has traditionally been the language of mathematics itself; when other languages (for example, philosophy and logic) have been used, they have been languages highly dependent on, or derived from, mathematics. By contrast, social talk takes priority over technical mathematical talk when we consider mathematics in sociological terms.
